# HW4 - ECE 402 Communications Engineering Homework 4(Fall...

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ECE 402: Communications Engineering Homework 4 (Fall 2009) Due: *Thursday* 10/15 1. Students graduating from NCSU have a mean GPA of 3.05, with a standard deviation of 0.50. (a) If student GPAs follow the Gaussian distribution, what percentage of students will graduate Summa Cum Laude (GPA 3 . 75)? (b) What percentage of students graduate Magna Cum Laude (3 . 5 GPA < 3 . 75)? Hint: The table of Gaussian probabilities on the course reference sheet could be useful. 2. The random telegraph process X ( t ) is a stationary ergodic random process with zero mean and autocorrelation R ( τ ) = A exp( - 2 λ | τ | ) . Find the PSD of X ( t ). 3. Let X ( t ) be a zero-mean stationary Gaussian noise process with PSD P X ( f ) = 1. Suppose Y ( t ) is obtained by passing X ( t ) through an ideal lowpass ﬁlter with unit gain and bandwidth 100 Hz. ( ) X t ( ) H f ( ) Y t (a) Find the autocorrelation and power spectral density of Y ( t ). (b)

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## This note was uploaded on 01/28/2012 for the course ECE 402 taught by Professor Townsend during the Fall '08 term at N.C. State.

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HW4 - ECE 402 Communications Engineering Homework 4(Fall...

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